【作者】 白玲；

【导师】 李大鸣；

【作者基本信息】 天津大学 ， 水力学及河流动力学， 2014， 博士

【摘要】 自然界的绝大部分物质,都以固态、液态和气态这三种聚集态存在。聚集态相变问题是涉及到宏观和微观、物理和化学方面的重要研究内容。范德瓦尔斯状态方程描述了粒子间远距离相互吸引、近距离相互排斥的作用力,不仅能够描述气相、液相共存以及气液相变,而且能够用于描述两相界面处的表面张力。其中部分研究成果对气液两相流与水力机械表面的冲蚀问题、特殊材料表面的相变问题、多相流问题研究具有借鉴价值。光滑粒子流体动力学(SPH)方法是一种无网格的拉格朗日粒子计算方法。该方法一个粒子表征在连续性介质尺度上一定大小的体积的特性,与经典分子动力学方法和耗散粒子动力学方法思路相似,使得该方法能够利用描述粒子间作用力的状态方程来进行流体力学计算。本文采用SPH方法,结合范德瓦尔斯相变理论,进行了气液两相相互转化的研究。在SPH相变模型中,为了得到稳定合理的计算结果,需要将范德瓦尔斯状态方程中的吸引力和排斥力在运动方程中分别进行考虑,增大吸引力的光滑长度。采用在模型中添加一个核心斥力作用,以及人工黏性项作用等方法来改善SPH方法固有的应力不稳定问题。二维SPH模型中采用了流体粒子与壁面粒子间排斥作用的势能函数模拟疏水壁面排斥力,并与采用范德瓦尔斯状态方程模拟的表面张力相结合的作用模式。通过模拟两个静止的等体积液滴相互融合的过程,验证了计算模式在SPH方法中模拟液滴的表面张力中的适用性。采用该模式模拟液滴撞击疏水壁面过程,模拟结果与液滴撞击疏水壁面的实验结果比较吻合较好,表明表面张力和疏水壁面作用力处理模式对模拟液滴撞壁过程具有实际应用价值。通过模拟液滴在高温壁面的汽化现象,以及高温气体在冷壁面热传递作用下在壁面附近冷凝液滴的形成、长大与合并现象,验证了模型在模拟气液相变方面的有效性。采用水的范德瓦尔斯参数进行了三维相变模拟。通过模拟真空中一个尺度为40纳米左右,初始状态达到平衡的超临界范德瓦尔斯流体,形成冷凝液滴的过程对模型进行了进一步验证,结果表明达到稳定状态后形成冷凝液滴的密度与理论值接近。为了求得三维范德瓦尔斯流体的相变图,分别计算了不同温度下液相和气相的密度值,绘制出SPH模拟得到的相变图,与理论推导得的相变图基本一致。为了验证模型在不同的温度变化方向上的适用性,分别采用了将单相冷凝液滴升温至特定的气液共存温度,以及将超临界流体降温至该气液共存温度这两种算例进行了比较,得到的结果基本一致。模型中同时还考虑了不同初始密度条件,证明了在一定的密度范围内,初始密度的不同基本不影响计算结果。更多还原

【Abstract】 Most matters in nature exist in forms of solid, liquid and gas. Phase change is an important research topic which is commonly seen in physics and chemistry from macro-scale to micro-scale. The van der Waals(vdW) equation describes the long-range attractive force and short-range repulsive force between particles. The vdW equation can not only explain the coexistence of liquid and vapor, and liquid-vapor phase transition, but also describe the surface tension between the two phases. Some of the results can be used to study the erosion of the hydraulic machinery surface from the liquid-gas two-phase flow, the phase change on the special material surfaces, and the multi-phase flow.Smoothed particle hydrodynamics(SPH) is a purly meshfree Lagrangian particle method. The feature that each SPH particle represents a certain volume in continue scale, which is similar to classical molecular dynamic methond and dissipative particle dynamics, makes it possible to use the inter-particle equation of state to do fluid mechanics calculation. The vdW equation of state is used in SPH method to study the liquid-vapor phase transition. In order to get stable and reasonable results, the smoothing length of the attractive force should be larger than that of the repulsive force. To avoid the stress instability which is inherent in SPH method, a core repulsive force and the artificial viscosity are used here.Combined with a potential function that describes the repulsive force between liquid and the surface, the van der Waals equation of state is used in the 2D SPH model as a surface tension model. The surface tension model is validated by simulating the coalescence of two equally sized static droplets in vacuum. The model is used in simulating the phenomenon of liquid droplet impact on hydrophobic surface, and the simulated results are in good agreement of the related experimental results, indicating that the scheme we treat the surface tension and the repulsive force of the hydrophobic surface is effective and applicable in droplet impact surface problems. The 2D model is also used in simulating the vaporization of two droplets on hot surface, and the condensation of vapor near the cold walls. The formation, growth and coalescence of the condensed droplet are captured in the simulation, which reveals that the model is able to do phase change simulations.The 3D SPH phase change model is parameterized for water. The model is first validated by forming a condensed liquid drop from a 3D 40-nanometer supercritical fluid system. The liquid density is close to the theoretical value after equilibrium. In order to get a liquid-vapor phase diagram, the densities of liquid and vapor at different temperatures are calculated, and the model reproduces a phase diagram which is consistent with the theoretical one. By heating a liquid drop to a coexistent temperature and cooling the supercritical gas to the same coexistence temperature, the effects of temperature change direction is compared and the comparison shows that for the same target temperature, different temperature change direction barely affect the simulated results. Also, within the threshold of the density, the model is able to get same liquid and vapor densities for different initial density conditions.更多还原